Event Horizon, 24 Nov 2003

1
Quantum ComputingHarnessing quantum mechanics
for information technology

• Andrew Fisher
• UCL

2
Overview

• Whats different about a quantum computer?
• How can quantum mechanics help with information
  processing?
• How can quantum parallelism make a difference
  to the way computations are done?
• How might a quantum computer actually be built?
• What are we doing at UCL?

3
Overview

• Whats different about a quantum computer?
• How can quantum mechanics help with information
  processing?
• How can quantum parallelism make a difference
  to the way computations are done?
• How might a quantum computer actually be built?
• What are we doing at UCL?

4
Why we need quantum mechanics for more of the
same

• Moores Law (doubling of transitors per chip
  every 2 years) already takes mainstream
  electronics into regions where quantum mechanics
  is important
• Transistors with gate lengths of 10nm can
  already be fabricated
• Wave-like quantum properties of electrons become
  important on this lengthscale
• Transistors switchable by a single electron
  predicted by 2015 or so

Quantum mechanics is crucial - but this is not
what we mean by quantum computing
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How is quantum mechanics different?
A classical system is always (in principle) in a
definite state we just have to specify which
one.
For example, to give a complete specification of
the system of N particles, we just have to
specify the positions and velocities (or
positions and momenta) of all of them 6N
variables in all.
But for a quantum system this is not true
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How is quantum mechanics different? (2)
The state of a quantum system can involve many
different possibilities simultaneously.
Examples
A double slit experiment particles pass through
both slits to create interference pattern
A particle moving in a potential well has a
probability of being found at many different
positions
The spin of a particle for example an
electron can be both up and down
simultaneously
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Quantum mechanics and kets
Mathematically, represent state of the system
using kets (a notation introduced by Dirac).
A ket represents the state of a system,
independently of the details of what coordinate
system we use.
Basis kets represent a complete set of
possible states for system
Compare a two-dimensional vector
Basis vectors represent a complete set of
possible directions
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Quantum mechanics and information
What does all this have to do with information
processing?
Information is physics.
It is not useful to separate abstract statements
about information content and information
processing from the physical representation of
that information.
For example we now know that computer science
classification of problems into hard and easy
depends on the physical laws used to process the
information.
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What is quantum computing?
Classical bits
Quantum bits
Superposition of 0 and 1
(qubits)
A quantum computer performs manipulations on
information represented as quantum bits, just as
a classical computer performs manipulations on
information represented as classical bits.
A quantum computer could perform certain tasks
(much) more efficiently than using any known
algorithm on a classical computer. It would mark
the transition from passively observing the
quantum regime, to controlling it.
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Overview

• Whats different about a quantum computer?
• How can quantum mechanics help with information
  processing?
• How can quantum parallelism make a difference
  to the way computations are done?
• How might a quantum computer actually be built?
• What are we doing at UCL?

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Why the advantage?
Have to specify much more information to give the
state of a quantum system than of its classical
analogue.
E.g. Three qubits
Specifying general classical state requires three
binary numbers
Specifying general quantum state of N qubits
requires 2N numbers
Since quantum mechanics is linear, operations
can, in effect, be performed on each member of
this superposition in parallel.
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Quantum parallelism
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Quantum gates
The bits are processed by means of logical gates
QUANTUM
CLASSICAL
X
Y
Exclusive or or controlled not gate
And
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What could it do?

• A quantum computer could
• Factor large integers in a time exponentially
  faster than any known classical algorithm,
  thereby making known public-key cryptography
  protocols vulnerable to attack
• Search a database of N items in a time
  proportional to
• Efficiently simulate the behaviour of another
  quantum system
• Possibly run totally new algorithms that we
  cannot yet conceive because they have no
  classical analogue
• Lead to a new understanding of the transition
  between quantum and classical physics
• When can a macroscopic system be put into a
  superposition of quantum states?
• The nature of quantum entanglement and nonlocality

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What do we need?
Ability to perform any transformation on the
state of the quantum bits (like any rotation of
a vector). Needs, for example
At least one two-qubit manipulation that is
non-trivial in the sense that it produces
quantum correlations (entanglement) between the
qubits

Arbitrary one-qubit manipulations
(Hadamard gate)
all before decoherence sets in.
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A simple example
Is a particular coin we are given fair (heads
on one side, tails on the other) or not (both
sides the same)?
Equivalent to asking
Is a particular binary function that we are given
balanced (equally likely to give 0 or 1) or
constant (always gives same result)
Balanced
Constant
Classically must look at both sides of coin
(evaluate function twice)
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The Deutsch-Josza algorithm
Measure 0?constant 1?balanced
with just one function evaluation!
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Overview

• Whats different about a quantum computer?
• How can quantum mechanics help with information
  processing?
• How can quantum parallelism make a difference
  to the way computations are done?
• How might a quantum computer actually be built?
• What are we doing at UCL?

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The DiVincenzo Checklist

• Must be able to
• Characterise well-defined set of quantum states
  to use as qubits
• Prepare suitable states within this set
• Carry out desired quantum evolution (i.e. the
  computation)
• Avoid decoherence for long enough to compute
• Read out the results
• And ideally
• Transport qubits
• Interconvert stationary and flying qubits

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Some actual or proposed quantum computers
Liquid-state NMR (quantum computing in a coffee
cup - has factored 15)
Bose-Einstein condensates
Lattices of cold atoms
Atom/photon interactions in cavities (cavity
QED)
Ion traps
Superconducting circuits
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The solid state pros and cons for quantum
computing

• Potential advantages
• Scalability
• Silicon compatibility
• Microfabrication (and nanofabrication)
• Possibility of engineering structures
• Interaction with light (quantum communication)
• Potential disadvantage
• Much stronger contact of qubits with environment,
  so (usually) much more rapid decoherence

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The DiVincenzo Checklist

• Must be able to
• Characterise well-defined set of quantum states
  to use as qubits
• Prepare suitable pure states within this set
• Carry out desired quantum evolution
• Avoid decoherence for long enough to compute
• Read out the results
• And ideally
• Transport qubits
• Interconvert stationary and flying qubits

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What are the qubits?

• Many different particles in solids (electrons and
  nuclei) whose states can be used
• There are also collective excitations that only
  occur in many-particle systems
• Possible systems for qubits include
• Nuclear spins
• Nuclear (atomic) displacements
• Electron spins
• Electron charges
• Correlated many-electron states

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Timescales

• Can arrange these roughly according to strength
  of the qubit interactions with one another (and
  with the environment)

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Many-particle states superconductors

• Superconductors are an example of a macroscopic
  quantum state
• Coherence extending over large distances
• Use magnetic field (flux) through a
  superconducting ring as the qubit.

Superconducting loop with small weak link of
normal material (SQUID)
Field
Field
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Many-particle states superconductors

• Superconductors are an example of a macroscopic
  quantum state
• Coherence extending over large distances
• or use a small Cooper pair box containing
  variable number of superconducting electrons

Box connected to reservoir of superconducting
electrons by weak link

N electrons
(N2) electrons
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Coherence of qubits in superconductors
Oscillating population of single Cooper pair
box as two quantum processes interfere
Nakamura et al. Nature 398 786 (1999)
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Engineering the quantum states
Vion et al Science 296 886 (2002)
By working at saddle-point where system is
insensitive to noise
get quantum quality factor Q25,000
Entanglement of two qubits recently demonstrated
in a similar system (Mooij et al, Delft)
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Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

V0
Magnetic field
Si
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Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

V0

Magnetic field
Si
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Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

VJ
- - - - -
Si
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Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon
  crystal
• Evolution and measurement of qubits performed by
  controlling individual electron states nearby

VJ0

Si
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Nuclear spins - the Kane proposal

• Readout performed by transferring qubits to
  electrons and measuring small changes in the
  shape of the electron distribution

- - - - -
Electron cannot transfer
Si
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Nuclear spins - the Kane proposal

• Readout performed by transferring qubits to
  electrons and measuring small changes in the
  shape of the electron distribution

- - - - -
Electron transfers
Si
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Nuclear spins - the Kane proposal
20 nm
A-gates
J-gates
Now good progress on some fabrication issues
(Clark et al 2002)
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Overview

• Whats different about a quantum computer?
• How can quantum mechanics help with information
  processing?
• How can quantum parallelism make a difference
  to the way computations are done?
• How might a quantum computer actually be built?
• What are we doing at UCL?

37
The DiVincenzo Checklist

• Must be able to
• Characterise well-defined set of quantum states
  to use as qubits
• Prepare suitable pure states within this set
• Carry out desired quantum evolution
• Avoid decoherence for long enough to compute
• Read out the results
• And ideally
• Transport qubits
• Interconvert stationary and flying qubits

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Is there another way?
Would really like to control coupling of qubits
without presence of nearby electrodes and
associated electromagnetic fluctuations
Our proposal (Stoneham et al., UCL) use real
transitions in a localized state to drive gate
Exploit properties of point defect systems
conveniently occurring in Si
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Our proposal basic idea

• Qubits are S1/2 electron spins which must be
  controlled by one- and two-qubit gates
• The spins are associated with dopants (desirable
  impurities)
• Chosen so they do not ionise thermally at the
  working temperatures (deep donors)
• The dopants are spaced 7-10nm to have negligible
  interactions in the off state

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Basic Ideas (Continued)

• The new concept is to control the spins producing
  the A-gates and J-gates using laser pulses

• Another major new concept is separation of the
  storing of Quantum information from the control
  of Quantum interactions

• Uniquely, the distribution of dopant atoms is
  disordered
• A disordered distribution is desirable for system
  reasons
• Dopants do not have to be placed at precise sites

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Controlling Spins
Control gate by laser-induced electron transfer
Gate addressed by combination of position and
energy
Silicon
Source of Control Electron
Donors carrying Qubit Spins
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Controlling Spins
Control gate by laser-induced electron transfer
Gate addressed by combination of position and
energy
Silicon
Source of Control Electron
Donors carrying Qubit Spins
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Configuring the Device

• When we have made a device

• Some qubit atoms will be too close to use as
  gates
• - These may be useful to move quantum information
  around

• Some qubit atoms will be at useful spacings

• Some qubit atoms will be too distant (hence
  useless)

we shall not know in advance which are which!
The solution We shall configure each device,
just as hard disks are configured There are also
analogies with communications networks
Dopants
Silicon
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Can one achieve entanglement?

• Experimental demonstrations for related systems
• Optically-induced many-spin entanglement
  demonstrated in quantum wells
• Bao, Bragas, Furdyna, Merlin 2003 Nature
  Materials 2 175 (also 2003 Sol State Comm 127
  771)
• Entanglement demonstrated in bulk spin systems
  via macroscopic properties
• Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature
  425 48.

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Macroscopic properties (magnetic susceptibility)
of LiHo0.045Y0.955F4 showing effects of
entanglement.
Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature
425 48
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Advantages and challenges

• Advantages
• Compatibility with CMOS
• Coupling mechanism does not rely on a small
  energy scale, so potential for high-temperature
  operation if single-qubit decoherence OK
• An interface with photons (flying qubits) built
  in from the beginning
• Take advantage of natural inhomogeneity to
  address individual gates

• Challenges
• Initialization cannot be done using B-field if
  operate at high T
• Must ensure no residual entanglement between
  control particle and qubits (gate timing)
• Readout mechanisms
• Connectivity of gates
• Fabrication and demonstration experiments (London
  Centre for Nanotechnology)

New 3.5M Basic Technology project at UCL, 2003-7
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To watch

• The Basic Technology project
• Other quantum-information related projects in the
  CMMP group and in the new London Centre for
  Nanotechnology
• The new IRC in Quantum Information Processing
  (CMMP group and Sougato Bose involved)

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Thanks

• Several colleagues at UCL
• Marshall Stoneham
• Thornton Greenland
• Gabriel Aeppli
• Joe Gittings
• Robbie Rodriguez
• Members of informal quantum logic gate club
  (Oxford/Cambridge/HP/UCL/IC/Bristol)
• EPSRC and Basic Technology programme ()

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To find out more

• About the field in general
• Gerald Milburn The Feynman Processor (Perseus
  1998)
• Feynman lectures on computation (Penguin 1999)
• Michael Nielsen and Isaac Chuang Quantum
  computation and quantum information (CUP 2000
  for the serious and advanced student!)
• About our Basic Technology project
• Our paper Stoneham, Fisher and Greenland J.
  Phys. Cond. Matt. 15 L447 (2003) (find it on
  http//www.iop.org)
• Nature news article (31 July 2003 see also
  http//www.nature.com))
• About the LCN
• LCN website http//www.london-nano.ucl.ac.uk